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May 30, 2026Open Access

A review on quantum graphs: From mathematical foundations to applications

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Authors

KSKavya Mangattu SudheerNSNandhini Sivasubramaniam

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Overview

Review discusses quantum graphs modeling quantum dynamics, highlighting their applications in spectral theory and chaos.

Key Points

  • This review aims to explore the mathematical foundations and applications of quantum graphs in modeling quantum dynamics.
  • Examines self-adjoint operators and metric graph formalisms.
  • Considers developments in spectral theory relevant to quantum chaos and statistics.
  • Discusses stability analyses and extensions to various types of quantum graphs.
  • Quantum graphs effectively model spectral and transport phenomena in quantum dynamics.
  • Notable enhancements in spectrum theory aid in understanding quantum chaos and universal spectral statistics.
  • Identifies ongoing challenges in spectral invariants and random graph models.

Cite This Study

Sudheer et al. (2026) studied this question.

synapsesocial.com/papers/6a1a81e00307b78509433a91https://doi.org/10.30511/mcs.2025.2075553.1566
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